Quantisation of type IIB superstring theory and the matrix model

Abstract

We discuss the path-integral quantisation of perturbative string theory and show equivalence between the Polyakov-type, Schild-type and Nambu-Goto-type formulations of critical type II superstring theory in the Minkowski and Euclidean signatures. Remarkably, we also find that the Minkowskian path integral realises causality in the sense that a string does not propagate between points at space-like separation, by giving careful consideration to the measure of the world-sheet metric. We also discuss matrix regularisation of the path integral for type IIB perturbative superstring theory. The obtained matrix models are the Euclidean IKKT matrix model and a modified Minkowskian IKKT model, depending on how the matrix regularisation is applied.

arXiv comment28 pages; v3: minor corrections and footnotes added

References in corpus (21)

• M Theory As A Matrix Model: A Conjecture
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• A Large-N Reduced Model as Superstring
• Space-Time Structures from IIB Matrix Model
• Monte Carlo Approach to M-Theory
• Convergent Yang-Mills Matrix Theories
• Describing Curved Spaces by Matrices
• String Field Theory from IIB Matrix Model
• Schild Action and Space-Time Uncertainty Principle in String Theory
• Towards a Non-perturbative Formulation of IIB Superstrings by Matrix Models
• Vertex Operators for the Supermembrane
• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Progress in the numerical studies of the type IIB matrix model
• Vertex Operators in IIB Matrix Model
• Higher-spin gravity and torsion on quantized space-time in matrix models
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Quantization of the Relativistic Particle
• Supersymmetric Wilson Loops in IIB Matrix Model
• Wilson Loops and Vertex Operators in Matrix Model
• Private life of the Liouville field that causes new anomalies in the Nambu-Goto string
• Progress toward the Determination of Complete Vertex Operators for The IIB Matrix Model